Finite Group Databasebeta

← Group #424596

Character table — Group #424596

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12224444222222444444444422224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-1
χ311111111111111111111111111-1-111-1-111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111
χ5111111111111111111111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ911111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ1011111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ1211111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-111-1-111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1111111-1-111-1-1
χ17222222222-2-2-2-2222-2-2-2-222220000000022-2-200000000-2-20000000000002-200000000
χ18222222222-2-2-2-2222-2-2-2-2222200000000-2-22200000000-2-2000000000000-2200000000
χ19222222222-2-2-2-2222-2-2-2-2-2-2-2-20000000022-2-20000000022000000000000-2200000000
χ20222222222-2-2-2-2222-2-2-2-2-2-2-2-200000000-2-22200000000220000000000002-200000000
χ212222-2-2-2-2222222-2-2-2-2-2-20000000000002-22-222-2-200000022-2-2000000000000000000
χ222222-2-2-2-2222222-2-2-2-2-2-20000000000002-22-2-2-222000000-2-222000000000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-2000000000000-22-2222-2-2000000-2-222000000000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-2000000000000-22-22-2-22200000022-2-2000000000000000000
χ252222-2-2-2-22-2-2-2-22-2-2222200002200-2-2002-2-220000000000000022-2-200000000000000
χ262222-2-2-2-22-2-2-2-22-2-2222200002200-2-200-222-200000000000000-2-22200000000000000
χ272222-2-2-2-22-2-2-2-22-2-222220000-2-20022002-2-2200000000000000-2-22200000000000000
χ282222-2-2-2-22-2-2-2-22-2-222220000-2-2002200-222-20000000000000022-2-200000000000000
χ292222-2-2-2-2-22-22-2-2222-22-22i2i−2i−2i000000000000000022-2-22i−2i00000000000000002i−2i0000
χ302222-2-2-2-2-22-22-2-2222-22-22i2i−2i−2i0000000000000000-2-2222i−2i0000000000000000−2i2i0000
χ312222-2-2-2-2-22-22-2-2222-22-2−2i−2i2i2i000000000000000022-2-2−2i2i0000000000000000−2i2i0000
χ322222-2-2-2-2-22-22-2-2222-22-2−2i−2i2i2i0000000000000000-2-222−2i2i00000000000000002i−2i0000
χ332222-2-2-2-2-2-22-22-222-22-222i2i−2i−2i002200-2-2000000000000−2i2i000000000000002i−2i000000
χ342222-2-2-2-2-2-22-22-222-22-222i2i−2i−2i00-2-20022000000000000−2i2i00000000000000−2i2i000000
χ352222-2-2-2-2-2-22-22-222-22-22−2i−2i2i2i002200-2-20000000000002i−2i00000000000000−2i2i000000
χ362222-2-2-2-2-2-22-22-222-22-22−2i−2i2i2i00-2-200220000000000002i−2i000000000000002i−2i000000
χ3722-2-222-2-2222-2-2-22-22-2-2200002-22-22-22-2000000000000000000000000000000002-200
χ3822-2-222-2-2222-2-2-22-22-2-2200002-2-222-2-2200000000000000000000000000000000-2200
χ3922-2-222-2-2222-2-2-22-22-2-220000-222-2-222-200000000000000000000000000000000-2200
χ4022-2-222-2-2222-2-2-22-22-2-220000-22-22-22-22000000000000000000000000000000002-200
χ4122-2-222-2-2-2-222-22-2222-2-2000000000000000000002i−2i2i−2i002-22-20000002i−2i0000000000
χ4222-2-222-2-2-2-222-22-2222-2-2000000000000000000002i−2i2i−2i00-22-22000000−2i2i0000000000
χ4322-2-222-2-2-2-222-22-2222-2-200000000000000000000−2i2i−2i2i002-22-2000000−2i2i0000000000
χ4422-2-222-2-2-2-222-22-2222-2-200000000000000000000−2i2i−2i2i00-22-220000002i−2i0000000000
χ4522-2-2-2-2222-2-222-2-222-2-2200002-200-2200000000002i−2i−2i2i00000000000000000000002i−2i
χ4622-2-2-2-2222-2-222-2-222-2-2200002-200-220000000000−2i2i2i−2i0000000000000000000000−2i2i
χ4722-2-2-2-2222-2-222-2-222-2-220000-22002-200000000002i−2i−2i2i0000000000000000000000−2i2i
χ4822-2-2-2-2222-2-222-2-222-2-220000-22002-20000000000−2i2i2i−2i00000000000000000000002i−2i
χ4922-2-2-2-222-2-222-222-2-2-2220000002-200-22000000000000002-2-2200002-2000000000000
χ5022-2-2-2-222-2-222-222-2-2-2220000002-200-2200000000000000-222-20000-22000000000000
χ5122-2-2-2-222-2-222-222-2-2-222000000-22002-2000000000000002-2-220000-22000000000000
χ5222-2-2-2-222-2-222-222-2-2-222000000-22002-200000000000000-222-200002-2000000000000
χ5344444444-44-44-4-4-4-4-44-44000000000000000000000000000000000000000000000000
χ5444444444-4-44-44-4-4-44-44-4000000000000000000000000000000000000000000000000
χ5544-4-444-4-44-4-444-44-4-444-4000000000000000000000000000000000000000000000000
χ5644-4-444-4-4-44-4-444-44-4-444000000000000000000000000000000000000000000000000
χ5744-4-4-4-444444-4-4-4-44-444-4000000000000000000000000000000000000000000000000
χ5844-4-4-4-444-44-4-4444-444-4-4000000000000000000000000000000000000000000000000
χ594-44-44i−4i4i−4i0000000000002+2i−2−2i2−2i−2+2i0000000000002-22i−2i00000000002-22i−2i00000000000000
χ604-44-44i−4i4i−4i0000000000002+2i−2−2i2−2i−2+2i000000000000-22−2i2i0000000000-22−2i2i00000000000000
χ614-44-44i−4i4i−4i000000000000−2−2i2+2i−2+2i2−2i0000000000002-22i−2i0000000000-22−2i2i00000000000000
χ624-44-44i−4i4i−4i000000000000−2−2i2+2i−2+2i2−2i000000000000-22−2i2i00000000002-22i−2i00000000000000
χ634-44-4−4i4i−4i4i0000000000002−2i−2+2i2+2i−2−2i0000000000002-2−2i2i00000000002-2−2i2i00000000000000
χ644-44-4−4i4i−4i4i0000000000002−2i−2+2i2+2i−2−2i000000000000-222i−2i0000000000-222i−2i00000000000000
χ654-44-4−4i4i−4i4i000000000000−2+2i2−2i−2−2i2+2i0000000000002-2−2i2i0000000000-222i−2i00000000000000
χ664-44-4−4i4i−4i4i000000000000−2+2i2−2i−2−2i2+2i000000000000-222i−2i00000000002-2−2i2i00000000000000
χ678-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).